Embodied-Minds-Lab

Embodied-Minds-Lab / BES

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We propose Bidirectional Evolutionary Search (BES), a search framework that couples forward candidate evolution with backward goal decomposition.

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76
6
89% credibility
Found May 31, 2026 at 76 stars -- GitGems finds repos before they trend. Get early access to the next one.
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AI Analysis
Python
AI Summary

BES (Bidirectional Evolutionary Search) is a research project that uses AI to solve complex mathematical optimization problems. The system combines two approaches: it breaks down problems into smaller goals while simultaneously generating and evolving candidate solutions. Users can run the system to solve three types of problems—packing circles in squares, packing circles in rectangles, and placing points to maximize triangle areas. The system generates programs that represent solutions, evaluates them against mathematical constraints, and uses AI to evolve better solutions over time. Results are saved as executable code that can be verified and reused.

How It Works

1
🔍 You discover AI solving math problems

You hear about a research project where AI can solve complex mathematical puzzles like packing circles into shapes.

2
📚 You explore the project

You look at the documentation and see it can tackle three challenging problems: packing circles in squares, packing circles in rectangles, and placing points to maximize triangle areas.

3
🔗 You connect your AI service

You set up access to an AI service by adding your account information, so the system can use AI to think and generate solutions.

4
🚀 You launch the solver

With everything ready, you start the system and watch as it generates potential solutions, evaluates them, and evolves better ones.

5
The system evolves solutions
🔍
Backward search decomposes goals

The system breaks down the problem into smaller sub-goals to guide its search

🔀
Forward search evolves candidates

The system generates variations and combinations of existing solutions

6
📊 You see results appear

The system saves its best solutions as working programs, showing the circle positions and radii it discovered.

🎉 You achieve excellent solutions

The system finds solutions that rival or exceed human performance on these mathematical challenges, like packing circles with a total radius sum of 2.632.

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AI-Generated Review

What is BES?

BES (Bidirectional Evolutionary Search) is a research framework for self-improving language models through search. It combines two approaches: forward evolution generates candidate solutions, while backward decomposition breaks down goals into checkable sub-goals. The project focuses on inference-time problem solving across three mathematical benchmarks—circle packing in squares and rectangles, and the Heilbronn convex problem—achieving state-of-the-art results compared to other open-source evolutionary search methods.

The system is written in Python and built on top of ShinkaEvolve for the inference pipeline. It supports multiple LLM providers including OpenAI, Anthropic, Gemini, and DeepSeek, allowing developers to plug in different backends for experimentation. Results are provided as generated Python programs that solve each benchmark.

Why is it gaining traction?

The key differentiator is the bidirectional approach—most search methods rely purely on forward expansion, but BES adds backward goal decomposition to guide exploration more efficiently. This combination outperforms alternatives like OpenEvolve, GEPA, and ShinkaEvolve on the benchmarks tested, with the paper published on arxiv providing solid academic backing.

For developers interested in LLM-based code generation for optimization problems, this offers a concrete implementation with reproducible results and pre-generated solutions.

Who should use this?

This is primarily for researchers exploring LLM self-improvement techniques or evolutionary search algorithms. If you're working on mathematical optimization problems and want to generate solutions using language models, the benchmark implementations provide a useful starting point. Production use cases would require significant adaptation—the code is research-grade with limited documentation.

Verdict

BES shows promising results with a strong academic foundation, but at 76 stars it's an early-stage research project. The credibility score of approximately 90% reflects solid methodology, though the codebase lacks the polish of mature projects. If you're doing academic research in this space, it's worth studying; for production applications, wait for more developed implementations.

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